Something I assume the Rays understand: From here on out, they project to be perhaps the best team in the American League East. Something else I assume the Rays understand: They’ve dug themselves into too deep a hole, so this year the playoffs presumably aren’t in the cards. And that’s why we’re probably going to see the Rays trade David Price within the next couple weeks. He can help them only so much in 2014, he’ll be difficult for them to afford in 2015 and pieces received in return could replenish what’s become an emptier system than usual. This is how the Rays do the Rays. Price’s status is no kind of secret.

Given how good Price is — and given how many teams consider themselves to be in the playoff hunt — the lefty has a number of potential suitors. Price is the premier impact player available, so no one out there can shift the balance like he can. He might be worth 2 WAR in the final two-and-a-half months; then there’s the playoff bonus, to say nothing of 2015. It’s pretty easy to plug in numbers and see how Price could improve any rotation. But how do those improvements translate to changes in the odds?

Another way of asking the same question: Who might stand to benefit the most — in 2014 — from acquiring a guy like David Price?

Everything you’re going to see here is an estimate. In college, in analytical chemistry, we were instructed to count up all the various potential sources of error in an experiment and measurement. There are very real sources of error here. We don’t know how confident we can be about Price’s rest-of-season projection. We don’t know how confident we can be about the rest of the projections. We don’t know how confident we can be about the rest-of-season simulator. We don’t know how confident we can be about the Price improvement in each given staff. Every additional source of error makes the error bars a little bit wider, so I implore you to see these as less like numbers and more like ideas.

Now then, a chart is going to follow, featuring a dozen contenders. I’ve included each team that’s so much as been whispered as a possible Price destination, and then one or two others just for my own enlightenment. Some of these teams are far more likely to end up with Price than others, as, for example, the Angels almost certainly aren’t going to get anything like this completed. I figure it’s better to have too much information than not enough.

The chart shows differences in odds, by percentage points. The starting points are the current odds. The other points are those odds with a fresh, new David Price in the rotation, starting this week. So what you’re seeing are Price odds — current odds. I had to call on David Appelman for help, since he runs the simulator, and in order to set him up, I needed to make some guesses about how Price would fit in with each staff. To make room for Price, I had to take innings away from other guys, and this is another one of those potential sources of error. I also had to estimate Price projections in various ballparks and leagues, so there’s more potential error. Again: error. These numbers are very far from perfect, but they should at least convey more or less the right ideas. So, let’s get into this.

In blue, we’ve got gains in playoff odds (by percentage points). In red, we’ve got gains in division-series odds, which means odds of getting past a one-game playoff. And in black, we’ve got gains in odds of winning it all. Every single team, of course, would be improved by adding David Price, because David Price is one of the best pitchers in baseball. But all those teams would improve differently.

By regular playoff odds, no one would stand to benefit more than the Blue Jays, which we’ve got gaining about +16%. I shouldn’t need to remind you of all the potential sources of error, but that seems sensible enough to me, as the Jays are in a tight race for the AL East lead and for the Wild Card. Unsurprisingly, the Jays are said to be in the market for front-level starters, even though lately they’ve been more damaged by injuries to the position players.

It’s the same with getting to a full series. No one would stand to benefit more than the Blue Jays, which we’ve got gaining about +15%. For Toronto, the bulk of the improvement comes from improved odds of winning the division. It’s the Mariners who’d have the biggest gain in terms of winning the Wild Card, and the Wild Card leads to the next round half the time. But there’s a belief out there that it’s not worth selling out if you think your season is going to come down to one game.

And then there’s the matter of championship odds. We’re dealing with smaller magnitudes here, because the playoffs are hard and all the teams are good. In terms of winning the World Series, though, no one would stand to benefit more than the Dodgers, which we’ve got gaining almost +5%. Price wouldn’t do a ton to adjust the Dodgers’ odds of making the playoffs, since they’re already heavily favored to move on, but then you get to thinking about a playoff rotation that starts with Price, Clayton Kershaw and Zack Greinke. By these numbers, Price would most help the Blue Jays, in terms of advancing. But in terms of finishing the job, he’d most help the Dodgers. The Dodgers, too, are unsurprisingly interested in Price’s services, and they have the pieces to get him if they want.

The Angels don’t seem like they’re genuine suitors. Neither do the Yankees, who are kind of screwed without Masahiro Tanaka. The Braves, the Brewers, the Giants, the Orioles and the Pirates would all be better with Price, but those are extremely unlikely landing spots. It seems like this might come down to the Jays, the Dodgers, the Mariners and the Cardinals, with the Indians as a dark horse. By playoff odds, the Jays would improve the most, the Dodgers would improve the least, and the other three teams are around the same place. By division-series odds, it’s the Jays, then the Cardinals, then the rest, with the Mariners bringing up the rear. Finally, in terms of the World Series, it’s the Dodgers, then the Jays and Cardinals, then the Indians and Mariners. Much of this feels intuitive, as it seems like the Indians and Mariners are more than one big piece away from having strong title hopes. The others are more like teams that could get over the top.

About the Blue Jays’ pursuit: It’s unsurprising, but it might cost them an in-division premium. Maybe that’s worth it, or maybe Toronto’s better off chasing Cole Hamels, or someone else. This is an opportunity for Toronto, but Price isn’t the only player on the market.

And that’s something to consider. This is about David Price. This doesn’t consider other, smaller improvements from other, smaller acquisitions. Nor does it consider that other teams in the race would be trying to make their own roster tweaks. So even if the Jays were to add Price, who’s to say the Orioles don’t do something, and the Mariners don’t do something, and the Indians don’t do something? The Price trade won’t actually be made in isolation, but it’s likely to be the biggest trade.

The last thing to keep in mind: These are the numbers right now, during the All-Star break. Once baseball resumes, situations change and the numbers begin to get a more obsolete. They won’t change that much over the course of a day or a series, but the sooner a team acts to acquire Price, the sooner it can have Price and put him in ballgames. Something like 10% playoff odds hang in the balance, on average. Price doesn’t make anybody a shoo-in, but that’s less about Price and more about the nature of baseball, a game that requires contributions from several players every single day if you’re a team looking to go anywhere.

David Price is almost certainly going to change his uniform in the weeks ahead. He’ll land with some contender that’s paid a sky-high tax, and the idea will be that Price will help the team drive to the playoffs and steamroll through them. There’s not a team out there that Price wouldn’t make a good deal better. But there are teams that would benefit more, and teams that would benefit less. It’s only one more thing to think about, as if navigating the trade deadline weren’t already complicated enough.